Multitemporal latent dynamical framework for hyperspectral images unmixing

Multitemporal hyperspectral unmixing can capture dynamical evolution of materials. Despite its capability, current methods emphasize variability of endmembers while neglecting dynamics of abundances, which motivates our adoption of neural ordinary differential equations to model abundances temporally. However, this motivation is hindered by two challenges: the inherent complexity in defining, modeling and solving problem, and the absence of theoretical support. To address above challenges, in this paper, we propose a multitemporal latent dynamical (MiLD) unmixing framework by capturing dynamical evolution of materials with theoretical validation. For addressing multitemporal hyperspectral unmixing, MiLD consists of problem definition, mathematical modeling, solution algorithm and theoretical support. We formulate multitemporal unmixing problem definition by conducting ordinary differential equations and developing latent variables. We transfer multitemporal unmixing to mathematical model by dynamical discretization approaches, which describe the discreteness of observed sequence images with mathematical expansions. We propose algorithm to solve problem and capture dynamics of materials, which approximates abundance evolution by neural networks. Furthermore, we provide theoretical support by validating the crucial properties, which verifies consistency, convergence and stability theorems. The major contributions of MiLD include defining problem by ordinary differential equations, modeling problem by dynamical discretization approach, solving problem by multitemporal unmixing algorithm, and presenting theoretical support. We conduct experiments with seven state-of-the-art researches on both synthetic and real datasets, our method achieves 0.243 (Formula presented) on synthetic dataset 1, outperforming MUFormer by 0.012. The results have validated the utility of our work. Our code will be available at https://github.com/Lab-PANbin